静水荷载作用下矩形薄板力学特性研究及其应用  

The mechanical properties and application of rectangular thin plates under hydrostatic pressure

作　　者：高俊 党发宁[1] 李海斌 马宗源 任劼[1] 

机构地区：[1]西安理工大学西北旱区生态水利国家重点实验室,西安710048 [2]中国水电建设集团十五工程局有限公司,西安710065

出　　处：《应用力学学报》2018年第5期1029-1036,共8页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(51679199);水利部公益性行业科研专项基金(201501034-04);陕西省科技统筹创新工程重点实验室项目(2014SZS15-Z01)

摘　　要：基于平面闸门研究了两种边界条件下矩形薄板在水荷载作用下的挠度、内力、应力的分布规律。利用单三角级数分别构造了两对边简支一边固支一边自由以及三边固支一边自由矩形薄板在水压力作用下的挠曲变形函数,并依据最小势能原理求解了挠曲变形函数系数,最后根据薄板小挠度弯曲理论得到了两种边界条件下矩形薄板的内力与应力函数,并对挠度、内力、应力的分布规律进行了比较分析。结果表明,在相同静水压力作用下,两对边简支一边固支一边自由和三边固支一边自由矩形薄板的挠度以及内力分布规律不尽相同,其中三边固支一边自由矩形薄板挠度及背水面出现的最大拉应力值较两对边简支一边固支一边自由矩形薄板的要小。Based on the plane gate, the distributions of deflection, internal force and stress of rectangular thin plates(loaded by hydrostatic pressure) under two kinds of boundary conditions are researched. Flexural deformation function of rectangular thin plates under hydrostatic pressure about two opposite edges simply supported, one edge clamped and one edge free(SCSF) and three sides clamped and one side free(CCCF) are established respectively by use of single trigonometric series. Then, flexural deformation function coefficients can be obtained by means of principle of minimum potential energy. At last, the internal force and the stress functions of rectangular thin plates under two boundary conditions can be obtained by using the small deflection bending theory of thin plate. And the distributions of deflection, internal force and stress are compared and analyzed. The results show that the distributions and data of deflection, internal force and stress of the SCSF rectangular thin plat and the CCCF rectangular thin plat are different under the same hydrostatic pressure. The deflection and the maximal tensile stress on the downstream face of CCCF rectangular thin plate is smaller than the maximal tensile stress on the downstream face of the SCSF rectangular thin plate.

关 键 词：矩形薄板 最小势能原理 挠曲函数 力学特性 

分 类 号：O343[理学—固体力学]